Number System

Answer:- Zero can be written in the form p/q , where p and q are integers and q is not equal to 0. Therefore, zero is a rational number.

Question: 2 :- Find six rational number between 3 and 4.

Answer -

You can notice that by calculating averages between two numbers we get a number which is exactly between these two numbers. This way you can go on calculating infinite numbers of numbers.

Question3: Find five rational numbers between 3/5 and 4/5

Question4: State if following statements are true or false:

(a) Every natural number is a whole number.

(b) Every integer is a whole number.

(c) Every rational number is a whole number.

Answer: (a) As natural number is all numbers starting from 1 and the whole number includes zero as well so this statement is true. On the other hand every whole number is not natural number as zero is not a natural number.

(b) Only positive integers are whole numbers.

(c) Rational numbers are not whole numbers as they are not complete.

Question5: Write the following in decimal form and comment on their kind of decimal expression.

Question6: Express the following in the form p/q , where p and q are integers and p is not 0

Put 9 for every non-zero digit in the denominator and zero for zero in the denominator.

Question7: What can the maximum number of digits be in the repeating block of digits in the decimal expression of 1/17 ?

A fraction in lowest terms with a prime denominator other than 2 or 5 (i.e. coprime to 10) always produces a repeating decimal. The period of the repeating decimal, 1⁄p, where p is prime, is either p − 1 (the first group) or a divisor of p − 1 (the second group).

Question8: What property a rational number must satisfy to have terminating decimal expression

Answer: If the denominator is either 2 or 5 as its factor then the result will be terminating decimal. As 10 is the product of 2 and 5 so to have terminating decimal 2 or 5 are required. If there is a prime number other than 2 or 5 in the denominator then the decimal can or cannot be treminating.